{"paper":{"title":"Graphs of bounded degree and the $p$-harmonic boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.FA","authors_text":"Michael J. Puls","submitted_at":"2008-06-18T19:45:34Z","abstract_excerpt":"Let $p$ be a real number greater than one and let $G$ be a connected graph of bounded degree. In this paper we introduce the $p$-harmonic boundary of $G$. We use this boundary to characterize the graphs $G$ for which the constant functions are the only $p$-harmonic functions on $G$. It is shown that any continuous function on the $p$-harmonic boundary of $G$ can be extended to a function that is $p$-harmonic on $G$. Some properties of this boundary that are preserved under rough-isometries are also given. Now let $\\Gamma$ be a finitely generated group. As an application of our results we chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3073","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}